Derivative problem that I thought would be easy

1. Nov 15, 2013

Loopas

I've attached a picture of the problem.

The problem asks from f'(0) of the function:

f(x)=e^(2x)*g(x)

g(0)=-5 and g'(0)=3 are given.

So the answer I came to was:

f'(x)=2e^(2x)*g'(x)

However, when I work out the numbers I get:

f'(0)=6

This is not right. So I figured I made a mistake a mistake when taking the derivative of f(x). Now I'm stuck because I'm not sure how to derive the function when g(x) isn't explicitly given.

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2. Nov 15, 2013

Dick

Yes, you made a mistake when taking the derivative of f(x). Use the product rule.

3. Nov 15, 2013

SqueeSpleen

The product rule say that:
$(f(x)g(x))'=f'(x)g(x)+f(x)g'(x)$
You did:
$(f(x)g(x))'=f'(x)g'(x)$
Which is incorrect.

4. Nov 15, 2013

Loopas

Wow, thanks guys. Sometimes sleep deprivation can do some crazy things.